Computational memory with cooperation among rows of processing elements and memory thereof

ABSTRACT

A computing device includes an array of processing elements mutually connected to perform single instruction multiple data (SIMD) operations, memory cells connected to each processing element to store data related to the SIMD operations, and a cache connected to each processing element to cache data related to the SIMD operations. Caches of adjacent processing elements are connected. The same or another computing device includes rows of mutually connected processing elements to share data. The computing device further includes a row arithmetic logic unit (ALU) at each row of processing elements. The row ALU of a respective row is configured to perform an operation with processing elements of the respective row.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority to U.S. provisional patent application Ser. No. 62/983,076 (filed Feb. 28, 2020), which is incorporated herein by reference.

BACKGROUND

Deep learning has proven to be a powerful technique for performing functions that have long resisted other artificial intelligence approaches. For example, deep learning may be applied to recognition of objects in cluttered images, speech understanding and translation, medical diagnosis, gaming, and robotics. Deep learning techniques typically apply many layers (hence “deep”) of neural networks that are trained (hence “learning”) on the tasks of interest. Once trained, a neural network may perform “inference”, that is, inferring from new input data an output consistent with what it has learned.

Neural networks, which may also be called neural nets, perform computations analogous to the operations of biological neurons, typically computing weighted sums (or dot products) and modifying the results with a memoryless nonlinearity. However, it is often the case that more general functionality, such as memory, multiplicative nonlinearities, and “pooling”, are also required.

In many types of computer architecture, power consumption due to physically moving data between memory and processing elements is non-trivial and is frequently the dominant use of power. This power consumption is typically due to the energy required to charge and discharge the capacitance of wiring, which is roughly proportional to the length of the wiring and hence to distance between memory and processing elements. As such, processing a large number of computations in such architectures, as generally required for deep learning and neural networks, often requires a relatively large amount of power. In architectures that are better suited to handle deep learning and neural networks, other inefficiencies may arise, such as increased complexity, increased processing time, and larger chip area requirements.

SUMMARY

According to one aspect of this disclosure, a computing device includes an array of processing elements mutually connected to perform single instruction multiple data (SIMD) operations, memory cells connected to each processing element to store data related to the SIMD operations, and a cache connected to each processing element to cache data related to the SIMD operations. A first cache of a first processing element is connected to a second cache of a second processing element that is adjacent the first processing element in the array of processing elements.

According to another aspect of this disclosure, a computing device includes a plurality of rows of processing elements to perform SIMD operations. The processing elements of each row are mutually connected to share data. The computing device further includes a row arithmetic logic unit (ALU) at each row of the plurality of rows of processing elements. The row ALU of a respective row is configured to perform an operation with processing elements of the respective row.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of an example computing device that includes banks of processing elements.

FIG. 2 is a block diagram of an example array of processing elements.

FIG. 3 is a block diagram of an example array of processing elements with a controller.

FIG. 4 is a block diagram of an example array of processing elements with a controller and memory.

FIG. 5 is a schematic diagram of example processing elements and related memory cells.

FIG. 6 is an equation for an example matrix multiplication carried out by the processing elements and memory cells of FIG. 5 .

FIG. 7A is a schematic diagram of an example state sequence of the processing elements and memory cells of FIG. 5 .

FIG. 7B is a schematic diagram of an example state sequence of the processing elements and memory cells of FIG. 5 .

FIG. 7C is a schematic diagram of an example generalized solution to movement of input vector components among a set of processing elements.

FIG. 8 is a flowchart of an example method of performing operations using processing elements and memory cells.

FIG. 9 is a block diagram of an example processing element and related memory cells.

FIG. 10 is a block diagram of an example of the neighbor processing element interconnect control of FIG. 9 .

FIG. 11 is a block diagram of an example processing element and associated memory arrangement.

FIG. 12 is a block diagram of an example two-dimensional array of processing banks connected to an interface.

FIG. 13 is a block diagram of an example processing element with zero detection and disabling functionality.

FIG. 14 is a block diagram of memory cells associated with a processing element, where the memory cells are configured in blocks and related caches.

FIG. 15 is a block diagram of an arrangement of memory cells and associated processing elements of FIG. 14 connected by memory-sharing switches.

FIG. 16 is a block diagram of an example zero disable circuit.

FIG. 17 is a block diagram of a cache arrangement to facilitate communications among memory allocated to different processing elements.

FIG. 18 is a block diagram of a computing device including an array of processing elements with cache and connections there-between.

FIG. 19 is a block diagram of a bank of rows of processing devices to provide row-based and bank-based computations.

DETAILED DESCRIPTION

The techniques described herein aim to improve computational memory to handle large numbers of dot-product and neural-network computations with flexible low-precision arithmetic, provide power-efficient communications, and provide local storage and decoding of instructions and coefficients. The parallel processing described herein is suitable for neural networks, particularly where power consumption is a concern, such as in battery-powered devices, portable computers, smartphones, wearable computers, smart watches, and the like.

FIG. 1 shows a computing device 100. The computing device 100 includes a plurality of banks 102 of processing elements. The banks 102 may be operated in a cooperative manner to implement a parallel processing scheme, such as a single instruction, multiple data (SIMD) scheme.

The banks 102 may be arranged in a regular rectangular grid-like pattern, as illustrated. For sake of explanation, relative directions mentioned herein will be referred to as up, down, vertical, left, right, horizontal, and so on. However, it is understood that such directions are approximations, are not based on any particular reference direction, and are not to be considered limiting.

Any practical number of banks 102 may be used. Limitations in semiconductor fabrication techniques may govern. In some examples, 512 banks 102 are arranged in a 32-by-16 grid.

A bank 102 may include a plurality of rows 104 of processing elements (PEs) 108 and a controller 106. A bank 102 may include any practical number of PE rows 104. For example, eight rows 104 may be provided for each controller 106. In some examples, all banks 102 may be provided with the same or similar arrangement of rows. In other examples, substantially all banks 102 are substantially identical. In still other examples, a bank 102 may be assigned a special purpose in the computing device and may have a different architecture, which may omit PE rows 104 and/or a controller 106.

Any practical number of PEs 108 may be provided to a row 104. For example, 256 PEs may be provided to each row 104. Continuing the numerical example above, 256 PEs provided to each of eight rows 104 of 512 banks 102 means the computing device 100 includes about 1.05 million PEs 108, less any losses due to imperfect semiconductor manufacturing yield.

A PE 108 may be configured to operate at any practical bit size, such as one, two, four, or eight bits. PEs may be operated in pairs to accommodate operations requiring wider bit sizes.

Instructions and/or data may be communicated to/from the banks 102 via an input/output (I/O) bus 110. The I/O bus 110 may include a plurality of segments.

A bank 102 may be connected to the I/O bus 110 by a vertical bus 112. Additionally or alternatively, a vertical bus 112 may allow communication among banks 102 in a vertical direction. Such communication may be restricted to immediately vertically adjacent banks 102 or may extend to further banks 102.

A bank 102 may be connected to a horizontally neighboring bank 102 by a horizontal bus 114 to allow communication among banks 102 in a horizontal direction. Such communication may be restricted to immediately horizontally adjacent banks 102 or may extend to further banks 102.

Communications through any or all of the busses 110, 112, 114 may include direct memory access (DMA) to memory of the rows 104 of the PEs 108. Additionally or alternatively, such communications may include memory access performed through the processing functionality of the PEs 108.

The computing device 100 may include a main processor (not shown) to communicate instructions and/or data with the banks 102 via the I/O bus 110, manage operations of the banks 102, and/or provide an I/O interface for a user, network, or other device. The I/O bus 110 may include a Peripheral Component Interconnect Express (PCIe) interface or similar.

FIG. 2 shows an example row 104 including an array of processing elements 108, which may be physically arranged in a linear pattern (e.g., a physical row). Each PE 108 includes an arithmetic logic unit (ALU) to perform an operation, such as addition, multiplication, and so on.

The PEs 108 are mutually connected to share or communicate data. For example, interconnections 200 may be provided among the array of PEs 108 to provide direct communication among neighboring PEs 108.

A PE 108 (e.g., indicated at “n”) is connected to a first neighbor PE 108 (i.e., n+1) that is immediately adjacent the PE 108. Likewise, the PE 108 (n) is further connected to a second neighbor PE 108 (n+2) that is immediately adjacent the first neighbor PE 108 (n+1). A plurality of PEs 108 may be connected to neighboring processing elements in the same relative manner, where n merely indicates an example PE 108 for explanatory purposes. That is, the first neighbor PE 108 (n+1) may be connected to its respective first and second neighbors (n+2 and n+3).

A given PE 108 (e.g., n+5) may also be connected to an opposite first neighbor PE 108 (n+4) that is immediately adjacent the PE 108 (n+5) on a side opposite the first neighbor PE 108 (n+6). Similarly, the PE 108 (n+5) may further be connected to an opposite second neighbor PE 108 (n+3) that is immediately adjacent the opposite first neighbor PE 108 (n+4).

Further, a PE 108 may be connected to a fourth neighbor PE 108 that is immediately adjacent a third neighbor PE 108 that is immediately adjacent the second neighbor PE 108. For example, the PE 108 designated at n may be connected to the PE designated at n+4. A connection of the PE 108 (n) to its third neighbor PE 108 (n+3) may be omitted. The fourth-neighbor connection may also be provided in the opposite direction, so that the PE 108 (n) connects to its fourth neighbor PE 108 at n−4 (not shown).

Still further, a PE 108 may be connected to a sixth neighbor PE 108 that is immediately adjacent a fifth neighbor PE 108 that is immediately adjacent the fourth neighbor PE 108. For example, the PE 108 designated at n may be connected to the PE designated at n+6. A connection of the PE 108 (n) to its fifth neighbor PE 108 (n+5) may be omitted. The sixth-neighbor connection may also be provided in the opposite direction, so that the PE 108 (n) connects to its sixth neighbor PE 108 at n−6 (not shown).

Again, a plurality of PEs 108 may be connected to neighboring processing elements in the above relative manner. The designation of a PE 108 as n may be considered arbitrary for non-endmost PEs 108. PEs 108 at the ends of the array may omit certain connections by virtue of the array terminating. In the example of each PE 108 being connected to its first, second, fourth, and sixth neighbor PEs 108 in both directions, the six endmost PEs 108 have differing connections.

With reference to FIG. 3 , endmost PEs 108 at one end of a row 104 may have connections 300 to a controller 106. Further, endmost PEs 108 at the opposite end of the row 104 may have a reduced number of connections 302. Additionally or alternatively, end-most PEs 108 of one bank 102 may connect in the same relative manner through the controller 106 and to PEs 108 of an adjacent bank 102. That is, the controller 106 may be connected between two rows 104 of PEs 108 in adjacent banks 102, where the two rows 104 of PEs 108 are connected in the same manner as shown in FIG. 2

With reference to FIG. 4 , a row 104 of PEs 108 may include memory 400 to store data for the row 104. A PE 108 may have a dedicated space in the memory 400. For example, each PE 108 may be connected to a different range of memory cells 402. Any practical number of memory cells 402 may be used. In one example, 144 memory cells 402 are provided to each PE 108. Note that in FIG. 4 the interconnections 200 among the PEs 108 and with the controller 106 are shown schematically for sake of explanation.

The controller 106 may control the array of PEs 108 to perform a SIMD operation with data in the memory 400. For example, the controller 106 may trigger the PEs 108 to simultaneously add two numbers stored in respective cells 402.

The controller 106 may communicate data to and from the memory 400 though the PEs 108. For example, the controller 106 may load data into the memory 400 by directly loading data into connected PEs 108 and controlling PEs 108 to shift the data to PEs 108 further in the array. PEs 108 may load such data into their respective memory cells 402. For example, data destined for rightmost PEs 108 may first be loaded into leftmost PEs and then communicated rightwards by interconnections 200 before being stored in rightmost memory cells 402. Other methods of I/O with the memory, such as direct memory access by the controller 106, are also contemplated. The memory cells 402 of different PEs 108 may have the same addresses, so that address decoding may be avoided to the extent possible.

Data stored in memory cells 402 may be any suitable data, such as operands, operators, coefficients, vector components, mask data, selection data, and similar. Mask data may be used to select portions of a vector. Selection data may be used to make/break connections among neighboring PEs 108.

Further, the controller 106 may perform a rearrangement of data within the array of PEs 108 by controlling communication of data through the interconnections 200 among the array of PEs 108. A rearrangement of data may include a rotation or cycling that reduces or minimizes a number of memory accesses while increasing or maximizing operational throughput. Other examples of rearrangements of data include reversing, interleaving, and duplicating.

In other examples, a set of interconnections 200 may be provided to connect PEs 108 in up-down (column-based) connections, so that information may be shared directly between PEs 108 that are in adjacent rows. In this description, interconnections 200 and related components that are discussed with regard to left-right (row-based) connections among PEs apply in principle to up-down (column-based) connections among PEs.

FIG. 5 shows an array of PEs 108 and related memory cells 402. Each PE 108 may include local registers 500, 502 to hold data undergoing an operation. Memory cells 402 may also hold data contributing to the operation. For example, the PEs 108 may carry out a matrix multiplication, as shown in FIG. 6 .

A matrix multiplication may be a generalized matrix-vector multiply (GEMV). A matrix multiplication may use a coefficient matrix and an input vector to obtain a resultant vector. In this example, the coefficient matrix is a four-by-four matrix and the vectors are of length four. In other examples, matrices and vectors of any practical size may be used. In other examples, a matrix multiplication may be a generalized matrix-matrix multiply (GEMM).

As matrix multiplication involves sums of products, the PEs 108 may additively accumulate resultant vector components d₀ to d₃ in respective registers 500, while input vector components a₀ to a₃ are multiplied by respective coefficients c₀₀ to c₃₃. That is, one PE 108 may accumulate a resultant vector component d₀, a neighbor PE 108 may accumulate another resultant vector component d₁, and so on. Resultant vector components d₀ to d₃ may be considered dot products. Generally, a GEMV may be considered a collection of dot products of a vector with a set of vectors represented by the rows of a matrix.

To facilitate matrix multiplication, the contents of registers 500 and/or registers 502 may be rearranged among the PEs 108. A rearrangement of resultant vector components d₀ to d₃ and/or input vector components a₀ to a₃ may use the direct interconnections among neighbor PEs 108, as discussed above. In this example, resultant vector components do to d₃ remain fixed and input vector components a₀ to a₃ are moved. Further, coefficients c₀₀ to c₃₃ may be loaded into memory cells to optimize memory accesses.

In the example illustrated in FIG. 5 , the input vector components a₀ to a₃ are loaded into a sequence of PEs 108 that are to accumulate resultant vector components do to d₃ in the same sequence. The relevant coefficients c₀₀, c₁₁, c₂₂, c₃₃ are accessed and multiplied by the respective input vector components a₀ to a₃. That is, a₀ and c₀₀ are multiplied and then accumulated as d₀, a₁ and c₁₁ are multiplied and then accumulated as d₁, and so on.

The input vector components a₀ to a₃ are then rearranged, as shown in the PE state sequence of FIG. 7A, so that a remaining contribution of each input vector components a₀ to a₃ to a respective resultant vector components d₀ to d₃ may be accumulated. In this example, input vector components a₀ to a₂ are moved one PE 108 to the right and input vector components a₃ is moved three PEs 108 to the left. With reference to the first and second neighbor connections shown in FIG. 2 , this rearrangement of input vector components a₀ to a₃ may be accomplished by swapping a₀ with a₁ and simultaneously swapping a₂ with a₃, using first neighbor connections, and then by swapping a₁ with a₃ using second neighbor connections. The result is that a next arrangement of input vector components a₃, a₀, a₁, a₂ at the PEs 108 is achieved, where each input vector component is located at a PE 108 that it has not yet occupied during the present matrix multiplication.

Appropriate coefficients C₀₃, c₁₀, c₂₁, c₃₂ in memory cells 402 are then accessed and multiplied by the respective input vector components a₃, a₀, a₁, a₂. That is, a₃ and c₀₃ are multiplied and then accumulated as d₀, a₀ and c₁₀ are multiplied and then accumulated as d₁, and so on.

The input vector components a₀ to a₃ are then rearranged twice more, with multiplying accumulation being performed with the input vector components and appropriate coefficients at each new arrangement. At the conclusion of four sets of multiplying accumulation and three intervening rearrangements, the accumulated resultant vector components d₀ to d₃ represent the final result of the matrix multiplication.

Rearrangement of the input vector components a₀ to a₃ allows each input vector component to be used to the extent needed when it is located at a particular PE 108. This is different from traditional matrix multiplication where each resultant vector component is computed to finality prior to moving to the next. The present technique simultaneously accumulates all resultant vector components using sequenced arrangements of input vector components.

Further, such rearrangements of data at the PEs 108 using the PE neighbor interconnections (FIG. 2 ) may be optimized to reduce or minimize processing cost. The example given above of two simultaneous first neighbor swaps followed by a second neighbor swap is merely one example. Additional examples are contemplated for matrices and vectors of various dimensions.

Further, the arrangements of coefficients c₀₀ to c₃₃ in the memory cells 402 may be predetermined, so that each PE 108 may access the next coefficient needed without requiring coefficients to be moved among memory cells 402. The coefficients c₀₀ to c₃₃ may be arranged in the memory cells 402 in a diagonalized manner, such that a first row of coefficients is used for a first arrangement of input vector components, a second row of coefficients is used for a second arrangement of input vector components, and so on. Hence, the respective memory addresses referenced by the PEs 108 after a rearrangement of input vector components may be incremented or decremented identically. For example, with a first arrangement of input vector components, each PE 108 may reference its respective memory cell at address 0 for the appropriate coefficient. Likewise, with a second arrangement of input vector components, each PE 108 may reference its respective memory cell at address 1 for the appropriate coefficient, and so on.

FIG. 7B shows another example sequence. Four states of a set of PEs 108 are shown with four sets of selected coefficients. Input vector components a₀ to a₃ are rotated so that each component a₀ to a₃ is used exactly once to contribute to the accumulation at each resultant vector component d₀ to d₃. The coefficients c₀₀ to c₃₃ are arranged so that the appropriate coefficient c₀₀ to c₃₃ is selected for each combination of input vector component a₀ to a₃ and resultant vector component d₀ to d₃. In this example, the input vector components a₀ to a₃ are subject to the same rearrangement three times to complete a full rotation. Specifically, the input vector component of an n^(th) PE 108 is moved right to the second neighbor PE 108 (i.e., n+2), the input vector component of the PE 108 n+1 is moved left (opposite) to its first neighbor PE 108 (i.e., n) in that direction, the input vector component of the PE 108 n+2 is moved right to the first neighbor PE 108 (i.e., n+3), and the input vector component of the PE 108 n+3 is moved left to the second neighbor PE 108 (i.e., n+1).

FIG. 7C shows a generalized solution, which is implicit from the examples discussed herein, to movement of input vector components among a set of PEs 108. As shown by the row-like arrangement 700 of input vector components a₀ to a_(i), which may be held by a row 104 of PEs 108, rotating information may require many short paths 702, between adjacent components a₀ to a_(i), and a long path 704 between end-most components a_(i) and a₀. The short paths are not a concern. However, the long path 704 may increase latency and consume additional electrical power because charging and charging a conductive trace takes time and is not lossless. The longer the trace, the greater the time/loss. The efficiency of a row 104 of PEs 108 is limited by its long path 704, in that power is lost and other PEs 108 may need to wait while data is communicated over the long path 704.

As shown at 710, a circular arrangement of PEs 108 may avoid a long path 704. All paths 712 may be segments of a circle and may be made the same length. A circular arrangement 710 of PEs 108 may be considered an ideal case. However, a circular arrangement 710 is impractical for manufacturing purposes.

Accordingly, the circular arrangement 720 may be rotated slightly and flattened (or squashed), while preserving the connections afforded by circular segment paths 712 and the relative horizontal (X) positions of the PEs, to provide for an efficient arrangement 720, in which paths 722, 724 connect adjacent PEs or skip one intermediate PE. As such, PEs 108 may be connected by a set of first-neighbor paths 722 (e.g., two end-arriving paths) and a set of second neighbor paths 724 (e.g., four intermediate and two end-leaving paths) that are analogous to circular segment paths 712 of a circular arrangement 710. The paths 722, 724 have much lower variance than the short and long paths 702, 704, so power may be saved and latency reduced. Hence, the arrangement 720 represents a readily manufacturable implementation of an ideal circular arrangement of PEs 108.

FIG. 8 shows a method 900 that generalizes the above example. The method 900 may be performed with the computing device 100 or a similar device. The method may be implemented by instructions executable by the device 100 or a controller 106 thereof. The instructions may be stored in a non-transitory computer-readable medium integral to the device 100 or controller 106.

At block 902, operands (e.g., matrix coefficients) are loaded into PE memory cells. The arrangement of operands may be predetermined with the constraint that moving operands is to be avoided where practical. An operand may be duplicated at several cells to avoid moving an operand between such cells.

At block 904, operands (e.g., input vector components) are loaded into PE registers. The operands to be loaded into PE registers may be distinguished from the operands to be loaded into PE memory cells, in that there may be fewer PE registers than PE memory cells. Hence, in the example of a matrix multiplication, it may be more efficient to load the smaller matrix/vector to the into PE registers and load the larger matrix into the PE memory cells. In other applications, other preferences may apply.

At block 906, a set of memory cells may be selected for use in an operation. The set may be a row of memory cells. For example, a subset of coefficients of a matrix to be multiplied may be selected, one coefficient per PE.

At block 908, the same operation is performed by the PEs on the contents of the selected memory cells and respective PE registers. The operation may be performed substantially simultaneously with all relevant PEs. All relevant PEs may be all PEs of a device or a subset of PEs assigned to perform the operation. An example operation is a multiplication (e.g., multiplying PE register content with memory cell content) and accumulation (e.g., accumulating the resulting product with a running total from a previous operation).

Then, if a subsequent operation is to be performed, via block 910, operands in the PE registers may be rearranged, at block 912, to obtain a next arrangement. A next set of memory cells is then selected at block 906, and a next operation is performed at block 908. For example, a sequence of memory cells may be selected during each cycle and operands in the PE registers may be rearranged to correspond to the sequence of memory cells, so as to perform a matrix multiplication. In other examples, other operations may be performed.

Hence, a sequence or cycle or operations may be performed on the content of selected memory cells using the content of PE registers that may be rearranged as needed. The method 900 ends after the last operation, via block 910.

The method 900 may be varied. In various examples, selection of the memory cells need not be made by selection of a contiguous row. Arranging data in the memory cells according to rows may simplify the selection process. For example, a single PE-relative memory address may be referenced (e.g., all PEs refer to their local memory cell with the same given address). That said, it is not strictly necessary to arrange the data in rows. In addition or alternatively, a new set of memory cells need not be selected for each operation. The same set may be used in two or more consecutive cycles. Further, overlapping sets may be used, in that a memory cell used in a former operation may be deselected and a previously unselected memory cell may be selected for a next operation, while another memory cell may remain selected for both operations. In addition or alternatively, the operands in the PE registers need not be rearranged each cycle. Operands may remain in the same arrangement for two or more consecutive cycles. Further, operand rearrangement does not require each operand to change location, in that a given operand may be moved while another operand may remain in place.

FIG. 9 shows an example PE 108 schematically. The PE 108 includes an ALU 1000, registers 1002, a memory interface 1004, and neighbor PE interconnect control 1006.

The ALU 1000 performs the operational function of the PE. The ALU 1000 may include an adder, multiplier, accumulator, or similar. In various examples, the ALU 1000 is a multiplying accumulator. The ALU 1000 may be connected to the memory interface 1004, directly or indirectly, through the registers 1002 to share information with the memory cells 402. In this example, the ALU 1000 is connected to the memory interface 1004 though the registers 1002 and a bus interface 1008.

The registers 1002 are connected to the ALU 1000 and store data used by the PE 108. The registers 1002 may store operands, results, or other data related to operation of the ALU 1000, where such data may be obtained from or provided to the memory cells 402 or other PEs 108 via the neighbor PE interconnect control 1006.

The memory interface 1004 is connected to the memory cells 402 and allows for reading/writing at the memory cells 402 to communicate data with the registers 1002, ALU 1000, and/or other components of the PE 108.

The neighbor PE interconnect control 1006 connects to the registers 1002 and controls communication of data between the registers 1002 and like registers of neighboring PEs 108, for example via interconnections 200 (FIG. 2 ), and/or between a controller (see 106 in FIG. 3 ). The neighbor PE interconnect control 1006 may include a logic/switch array to selectively communicate the registers 1002 to the registers 1002 of neighboring PEs 108, such as first, second, fourth, or sixth neighbor PEs. The neighbor PE interconnect control 1006 may designate a single neighbor PE 108 from which to obtain data. That is, the interconnections 200 may be restricted so that a PE 108 only at most listens to one selected neighbor PE 108. The neighbor PE interconnect control 1006 may connect PEs 108 that neighbor each other in the same row. Additionally or alternatively, a neighbor PE interconnect control 1006 may be provided to connect PEs 108 that neighbor each other in the same column.

The PE may further include a bus interface 1008 to connect the PE 108 to a bus 1010, such as a direct memory access bus. The bus interface 1008 may be positioned between the memory interface 1004 and registers 1002 and may selectively communicate data between the memory interface 1004 and either a component outside the PE 108 connected to the bus 1010 (e.g., a main processor via direct memory access) or the registers 1002. The bus interface 1008 may control whether the memory 402 is connected to the registers 1002 or the bus 1010.

The PE may further include a shifter circuit 1012 connected to the ALU 1000 and a wide-add bus 1014 to perform shifts to facilitate performing operations in conjunction with one or more neighbor PEs 108.

FIG. 10 shows an example of the neighbor PE interconnect control 1006. The neighbor PE interconnect control 1006 includes a multiplexer 1100 or similar switch/logic array and a listen register 1102.

The multiplexer 1100 selectively communicates one interconnection 200 to a neighbor PE 108 to a register 1002 used for operations of the PE 108 to which the neighbor PE interconnect control 1006 belongs. Hence, a PE 108 listens to one neighbor PE 108.

The listen register 1102 controls the output of the multiplexer 1100, that is, the listen register 1102 selects a neighbor PE 108 as source of input to the PE 108. The listen register 1102 may be set by an external component, such as a controller 106 (FIG. 3 ), or by the PE 108 itself.

FIG. 11 shows a diagram of an example PE 1500 and its associated memory 1502. The memory 1502 may be arranged into blocks, so that the PE 1500 may access one block at the same time that an external process, such as direct memory access, accesses another block. Such simultaneous access may allow for faster overall performance of a row, bank, or other device containing the PE, as the PE and external process can perform operations with different blocks of memory at the same time and there will be fewer occasions of the PE or external process having to wait for the other to complete its memory access. In general, PE access to memory is faster than outside access, so it is expected that the PE 1500 will be able to perform N memory operations to one block per one outside operation to the other block.

The memory 1502 includes two blocks 1504, 1506, each containing an array of memory cells 1508. Each block 1504, 1506 may also include a local I/O circuit 1510 to handle reads/writes to the cells of the block 1504, 1506. In other examples, more than two blocks may be used.

The memory 1502 further includes a global I/O circuit 1512 to coordinate access by the PE and external process to the blocks 1504, 1506.

The PE 1500 may include memory access circuits 1520-1526, such as a most-significant nibble (MSN) read circuit 1520, a least-significant nibble (LSN) read circuit 1522, an MSN write circuit 1524, and an LSN write circuit 1526. The memory access circuits 1520-1526 are connected to the global I/O circuit 1512 of the memory 1502.

The memory address schema of the blocks 1504, 1506 of memory 1502 may be configured to reduce latency. In this example, block 1504 contains cells 1508 with even addresses and the block 1506 contains cells 1508 with odd addresses. As such, when the PE 1500 is to write to a series of addresses, the global I/O circuit 1512 connects the PE 1500 in an alternating fashion to the blocks 1504, 1506. That is, the PE 1500 switches between accessing the blocks 1504, 1506 for a sequence of memory addresses. This reduces the chance that the PE 1500 will have to wait for a typically slower external memory access. Timing between block access can overlap. For example, one block can still be finishing latching data into an external buffer while the other block is concurrently providing data to the PE 1500.

FIG. 12 shows an example two-dimensional array 1600 of processing banks 102 connected to an interface 1602 via I/O busses 1604. The array 1600 may be grid-like with rows and columns of banks 102. Rows need not have the same number of banks 102, and columns need not have the same number of banks 102.

The interface 1602 may connect the I/O busses 1604 to a main processor, such as a CPU of a device that contains the array 1600. The interface 1602 may be a PCIe interface.

The interface 1602 and buses 1604 may be configured to communicate data messages 1606 with the banks 102. The interface 1602 may pump messages through the busses 1604 with messages becoming accessible to banks 102 via bus connections 1608. A bank 102 may read/write data from/to a message 1606 via a bus connection 1608.

Each bus 1604 includes two legs 1610, 1612. Each leg 1610, 1612 may run between two adjacent columns of banks 102. Depending on its column, a given bank 102 may have bus connections 1608 to both legs 1610, 1612 of the same bus 1604 or may have bus connections 1608 to opposite legs 1610, 1612 of adjacent busses. In this example, even columns (e.g., 0^(th), 2^(nd), 4^(th)) are connected to the legs 1610, 1612 of the same bus 1604 and odd columns (e.g., 1^(st), 3^(rd)) are connected to different legs 1610, 1612 of adjacent busses 1604.

In each bus 1604, one end of each leg 1610, 1612 is connected to the interface 1602, and the opposite end of each leg 1610, 1612 is connected to a reversing segment 1620. Further, concerning the direction of movement of messages on the bus 1604, one leg 1610 may be designated as outgoing from the interface 1602 and the other leg 1612 may be designated as incoming to the interface 1602. As such, a message 1606 put onto the bus 1604 by the interface 1602 may be pumped along the leg 1610, through the reversing segment 1620, and back towards the interface 1602 along the other leg 1612.

The reversing segment 1620 reverses an ordering of content for each message 1606, such that the orientation of the content of each message 1606 remains the same relative to the PEs of the banks 102, regardless of which side of the bank 102 the message 1606 is on. This is shown schematically as message packets “A,” “B,” and “C,” which are discrete elements of content of a message 1606. As can be seen, the orientation of the packets of the message 1606 whether on the leg 1610 or the leg 1612 is the same due to the reversing segment 1620. Without the reversing segment, i.e., with a simple loop bus, the orientation of the message 1606 on the return leg 1612 would be opposite.

FIG. 13 shows another example of a PE 2100 that may be used with any of the example banks of processing elements discussed herein.

The PE 2100 includes an ALU 2102, an array of resultant registers 2104, a resultant selector 2105, a hold register 2106, a zero disable 2110, a switch 2112, an input vector register 2114, an input zero detector 2116, neighbor PE interconnect control 2118, and a listen register 2120.

The ALU 2102 implements an operation on data in the input vector register 2114 and data in memory cells 2130 associated with the PE 2100. Examples of such operations include multiplying accumulation as discussed elsewhere herein. This may include, for example, multiplying matrix coefficients, which may be stored in memory cells 2130, by an activation vector, which may be stored in input vector register 2114. During such operation, the array of resultant registers 2104 may accumulate resultant vector components. The ALU 2102 may include one or more levels of multiplexor and/or a multiplier 2108.

Accumulation of results in resultant registers 2104 may be performed. That is, at a given time, the input vector register 2114 may be multiplied with selected coefficients from memory cells 2130 and the products may be accumulated at the resultant registers 2104 (e.g., a product is added to a value already in a resultant register). As such, for a particular value in the input vector register 2114, an appropriate value may be selected from memory cells 2130 for multiplication and an appropriate resultant register 2104 may perform the accumulation. This may implement any of the input vector cycling/shuffling described herein, such as discussed with respect to FIGS. 7A-7C.

The resultant selector 2105 selects a resultant register 2104 to write to the memory cells 2130.

The neighbor PE interconnect control 2118 may communicate values between the input vector register 2114 of the PE 2100 and an input vector register 2114 of a neighboring PE 2100. As such, the neighbor PE interconnect control 2118 is connected to a like element in neighboring PEs 2100 via interconnections 2132. For example, the neighbor PE interconnect control 2118 may be connected to first neighbor PEs 2100 on each side of the PE 2100, second neighbor PEs 2100 on each side of the PE 2100, fourth neighbor PEs 2100 on each side of the PE 2100, and/or sixth neighbor PEs 2100 on each side of the PE 2100. When no such neighbor PE exists in the bank to which the PE 2100 is provided, the neighbor PE interconnect control 2118 may be connected to respective PEs 2100 of a neighboring bank and/or to a controller. The neighbor PE interconnect control 2118 may be configured to rotate or shuffle input vector values as discussed elsewhere herein. The neighbor PE interconnect control 2118 may connect neighboring PEs 2100 in a row (left-right) of PEs 2100. Additionally or alternatively, a neighbor PE interconnect control 2118 may connect neighboring PEs 2100 in a column (up-down) of PEs 2100.

The neighbor PE interconnect control 2118 may include a logic/switch array to selectively communicate values among PEs 2100, such as the logic/switch arrays discussed elsewhere herein.

The neighbor PE interconnect control 2118 may designate a single neighbor PE 2100 from which to obtain data. That is, interconnections 2132 with neighbor PEs 2100 may be restricted so that a PE 2100 only at most listens to one selected neighbor PE 2100. The listen register 2120 controls from which, if any, PE 2100 that the neighbor PE interconnect control 2118 obtains data. That is, the listen register 2120 selects a neighbor PE 2100 as the source of input to the PE 2100.

The hold register 2106 may be set to disable computation by the ALU 2102. That is, data may be selected from memory 2130 and moved into/out of input vector register 2114 while the hold register 2106 at the same time ensures that the computation is not performed by the PE 2100, but may be performed by other PEs in the same row/column.

The zero disable 2110 controls the inputs to the multiplier 2108 to be unchanged when detecting that one or both intended inputs to the multiplier 2108 are zero. That is, should the intended inputs include a zero value for multiplication and accumulation, the zero disable 2110 holds the present input values as unchanged instead of providing the actual inputs that include the zero value. Multiplication by zero produces a zero product which does not need to be accumulated. As such, the zero disable 2110 saves energy, as the ALU 2102 uses significantly more energy when an input changes as opposed to when the inputs do not change.

The switch 2112 allows a selected resultant register 2104 or the input vector register 2114, via the input zero detector 2116, to be written to memory cells 2130. The switch 2112 allows data from the memory cells 2130 to be written to the listen register 2120. The switch 2112 allows one bit of data to be written to the hold register 2106. The switch 2112 allows data to be written to the input vector register 2114 through the input zero detector 2116. If switch 2112 is open, then the memory cells 2130 are connected to the multiplier 2108, without being loaded down by inputs of the input vector register 2114 and input zero detector 2116 or the resultant selector 2105.

The input zero detector 2116 detects whether the input vector register 2114 contains a value that is zero. Likewise, the memory cells 2130 may include OR logic 2134 to determine whether the selected value in the memory cells 2130 is zero. The OR logic 2134 provides an indication of a zero value. As such, when either (or both) of the input vector register 2114 and the selected value in the memory cells 2130 is zero, the zero disable 2110 controls both inputs from the input vector register 2114 and the selected value in the memory cells 2130 to appear to the ALU 2102 to be unchanged, thereby refraining from performing a needless multiplication and accumulation and saving power at the ALU 2102.

With reference to FIG. 14 , the memory cells 2130 associated with a PE 2100 may include blocks 2200, 2202 of memory cells and related caches 2204, 2206. In this example, a main memory block 2200 is associated with a cache 2204 and secondary memory blocks 2202 are each associated with a cache 2206. The caches 2204, 2206 communicate with the PE 2100 rather than the PE communicating with the memory blocks 2200, 2202 directly.

A cache 2204, 2206 may read/write to its memory block 2200, 2202 an amount of data that is larger than the amount communicated with the PE 2100. For example, a cache 2204, 2206 may read/write to its memory block 2200, 2202 in 16-bit units and may communicate with the PE 2100 in 4-bit units. As such, timing of read/write operations at the memory blocks 2200, 2202 may be relaxed. Thus, it is contemplated that the processing speed of the PE 2100 will govern operations of the PE 2100 with the memory cells 2130. Clocking of the memory cells 2130 can be increased to meet the needs of the PE 2100.

An isolation switch 2208 may be provided to isolate secondary memory blocks 2202 and their caches 2206 from the PE 2100. As such, the PE 2100 may be selectably connected to a smaller set of memory cells or a larger set of memory cells. When the isolation switch 2208 is closed, the PE 2100 may access the main memory block 2200 and the secondary memory blocks 2202, through the caches 2204, 2206, as a contiguous range of addresses. When the isolation switch 2208 is opened, the PE 2100 may only access the main memory block 2200, though its cache 2204, with the respective reduced range of addresses. Opening the isolation switch 2208 to reduce the amount of available memory to the PE 2100 may save energy. The isolation switch 2208 may be implemented by a switchable bus that connects the secondary caches 2206 to the PE 2100.

In this example, each cache 2204, 2206 includes OR logic to inform the PE 2100 as to whether the memory value selected by the PE 2100 is zero. As such, the above-discussed technique of refraining from changing ALU input values may be used to save power.

Further, in this example, the memory cells 2130 include working or scratch registers 2210 connected to the PE 2100 to provide temporary space for intermediate or larger-bit computations.

A memory-sharing switch 2214, 2218 may be provided to connect memory blocks 2200, 2202 of a PE 2100 to memory blocks 2200, 2202 of a neighboring PE 2100. The memory-sharing switch 2214, 2218 may be implemented as a switchable bus that connects the caches 2204, 2206 to respective caches 2204, 2206 of a set of memory cells 2130 associated with a neighboring PE 2100.

As shown in FIG. 15 , a left-right (row-based) memory-sharing switch 2214 may connect PE memory 2130 to a left/right neighbor PE memory 2130. Similarly, an up-down (column-based) memory-sharing switch 2218 may connect PE memory 2130 to an up/down neighbor PE memory 2130. Any number and combination of such memory-sharing switches 2214, 2218 may be provided to combine memory cells 2130 associated with individual PEs 2100 into a combined pool of memory cells 2130 associated with a group of PEs 2100.

Memory-sharing switches 2214, 2218 may be provided between groups of memory cells 2130 so that a maximum pool of memory cells 2130 is determined by hardware. Alternatively, memory-sharing switches 2214, 2218 may be provided between all memory cells 2130, and firmware or software may govern a maximum pool size, if any.

PEs 2100 can share memory in groups of two or four, in this example. If a PE fails, it can be skipped. An entire column of PEs can be labelled as bad if a particular PE in the column is bad, so as to avoid having to move data laterally around the bad PE. In FIG. 15 , for example, if the top center PE 2100 had failed, it and both the top and bottom center PEs can be labeled “bad” and be skipped. However, if the rightmost PEs were supposed to be grouped with the center PEs to share memory, this memory can no longer be shared due to the bad PEs. The rightmost PEs can also skip the bad column of PEs and share with the leftmost PEs. This can be achieved by each PE having a DUD register that can be written from SRAM. An application can then initially detect the bad or failed PEs, and set the DUD bits for the entire column of PEs of the broken PE. When SRAM is then to be shared in a group that contains a DUD column, the controller can read the DUD bit and skip over the PE in that column. Hence, if the center column of PEs had their DUD bit set, the rightmost PEs could still share SRAM with the leftmost PEs.

In other examples, if size and power restrictions are a concern, a maximum size of shared PEs may be enforced such as a two-by-two arrangement of four PEs. Groups of four PEs may have hardwired interconnections. In this example, the DUD bit disables an entire block of four PEs.

In still other examples, the hardware may be further simplified and memory sharing may not be omitted. The DUD bit may provide a way of turning off a PE to save power.

With reference back to FIG. 14 , caches 2204, 2206 may provide I/O capabilities, such as addressing and address mapping for a pool of memory cells 2130 as enabled by memory-sharing switches 2214, 2218. Further, caches 2204, 2206 may be configured to perform copy, move, or other operations as facilitated by memory-sharing switches 2214, 2218. That is, caches 2204, 2206 may be I/O enabled so as to communicate information with the respective PE 2100 and further to communicate information with any other caches 2204, 2206 connected by memory-sharing switches 2214, 2218. As such, data in memory cells 2130 may be copied, moved, or undergo other operation independent of operation of a PE 2100.

Further, the isolation switch 2208 may allow a PE 2100 to access its main memory block 2200 while memory-to-memory operations, enabled by secondary caches 2206 and memory-sharing switches 2214, 2218, are performed to share information in secondary memory blocks 2202 with neighboring memory. This may allow for greater operational flexibility and for reading/writing data to memory 2130 while allowing PEs 2100 to continue with their assigned computations.

FIG. 16 shows a zero disable circuit 2110 that may be used in PEs discussed elsewhere herein, such as the PE 2100 of FIG. 13 . The zero disable circuit 2110 reduces power consumption used by a multiplier and/or accumulator of the PE. Such power may be saved by disabling the multiplier and/or the accumulator when an input value “a” of an adjacent PE is zero and/or when a coefficient “c” at the present PE is zero. Power savings may be substantial when the PEs are part of a device that processes a neural network, as it is often the case that a significant number (e.g., 50%) of values in such processing are zeros. Further, neural network can be trained to have coefficients “c” that tend to be zero, such that specific training can enhance power savings.

In addition to input values “a” taken from an adjacent PE at 2132A and coefficients “c” taken from memory, the zero disable circuit 2110 also takes respective indicators of whether or not such values “a” and “c” are zero, as indicated by “a=0” and “c=0”, respectively.

Various components of the zero disable circuit 2110 operate according to a clock (“clk”).

The zero disable circuit 2110 includes a multiplier 2402 to multiply input value “a” and coefficient “c”. The multiplier 2402 includes cascading logic, operates asynchronously, and therefore does not operate according to the clock. The multiplier 2402 is triggered only if either or both of its inputs, i.e., the input value “a” and the coefficient “c”, change. Hence, if either or both of the inputs “a” and “c” is zero, then the inputs to the multiplier 2402 are held unchanged, so as to prevent the multiplier 2402 from computing a zero result that unnecessarily consumes power.

The zero disable circuit 2110 includes a transparent latch 2404. Input to the transparent latch 2404 includes coefficients “c” from memory associated with the PE (e.g., memory cells 2130 of FIG. 13 ). The transparent latch 2404 acts as a pass-through when its select line stays high, requiring minimal power. When the select line of the transparent latch 2404 is lowered, it latches the current value into a fixed state. This uses power, but occurs less frequently than a latch that is set at each clock cycle. The transparent latch 2404 is set if coefficient “c” or input value “a” is zero, and the multiplier 2402 consequently does not receive a change in the coefficient “c” value. Rather, the multiplier 2402 still receives the previous value of the coefficient “c”.

The input value “a” is handled similarly. The zero disable circuit 2110 includes a register 2114 to store an input value “a”, as may be received with data from an adjacent PE at 2132A. The zero disable circuit 2110 receives a value for “a” from an adjacent PE and does not latch this value of “a” if either “a” or “c” is zero. If the coefficient “c” is zero and the input value “a” is not zero (a!=0), then the input value “a” is stored, as the input value “a” may still need to be passed to the next adjacent PE at 2132B. The zero disable circuit 2110 includes a shadow register 2408 to transfer the input value “a” to the next PE at 2132B. The shadow register 2408 has a path parallel to the main register 2114 that stores the input value “a”. The shadow register 2408 is used to latch in the input value “a” if either “a” or “c” is zero.

The zero disable circuit 2110 further includes a demultiplexer 2414 at the outputs of the main register 2114 and shadow register 2408 to select which value to pass to the next PE at 2132B.

The shadow register 2408 is useful when the input value “a” is not zero (a!=0) and the coefficient “c” is zero. However, in this example, signal timing is simplified by also using the shadow register 2408 for the case where the input value “a” is zero and the coefficient “c” is zero.

When neither the input value “a” nor the coefficient “c” is zero, then the coefficient “c” flows from memory, through the transparent latch 2404, and to the multiplier 2402. Further, the input value “a” flows from the previous adjacent PE at 2132A through the main registers 2114, to the multiplier 2402, and also to the next adjacent PE at 2132B.

When either “a” or “c” are zero, the previous coefficient “c” from memory is held in the transparent latch 2404, and the previous input value “a” is held in the main register 2114. As such, the inputs to the multiplier 2402 do not change, and the multiplier 2402 is therefore not triggered, saving power.

The “a=0” signal from the previous adjacent PE at 2132A is held for one clock cycle, and then passed on to the next adjacent PE at 2132B.

When the input value “a” is not zero and the coefficient “c” is zero, then the contents of the shadow register 2408 is selected to be passed on to the next PE at 2132B. It is selected by a signal, delayed by one clock cycle, by a delay flipflop 2420, which holds the signal for the duration of one clock.

Further, in this example if the input value “a” is zero and the coefficient “c” is also zero, the input value “a” value of zero is latched to the shadow register 2408, although it is never used. This simplifies signal timing issues and may further save power. Such a zero value is not passed on to the next PE at 2132B, since the demultiplexer signal that selects between the main register 2114 and the shadow register 2408 is only triggered for the case where “c=0 and a!=0”. However, the “a=0” signal is passed on. This may save some power, since the previous value of the main register 2114 is passed on to the next PE at 2132B (along with the “a=0” signal that tells the next PE to ignore the actual input value “a”), and since the value has not changed, the signals in the conductors connecting the PEs do not have to change, which would otherwise cost power.

There are various examples where refraining from triggering an ALU can reduce computations and save power. In neural networks, layers of convolutions are often used. After each convolution, a scale factor (e.g., multiplying all the results by a common factor) is often applied to normalize data or to shift the data into a useable range. When using integer math, the scale factor may be performed as two steps: multiplication by a factor, and then a bit-shift. A bit-shift shifts the bits of a result rightwards, discarding the lower least significant bits.

Multiplication and shift values are often known in advance, as with the coefficients. If the multiplier value and shift value are such that some or many of the lower bits will be discarded, this means that some of the least significant terms are never used. Hence, two approaches may be used to save power: (1) a part of the output may be skipped (e.g., the lowest “little ‘a’ x little ‘c’” term) and/or (2) refrain from calculating the lowest term (e.g., “little ‘a’ x little ‘c’”) of the convolution at all. The first may save some cycles. The second may save many cycles. In an example that uses 4-bit PEs to perform 8-bit computations, up to ¼ of the convolution computation may be saved.

With regard to all examples herein, a power-saving floating point representation may be used. Power may be saved when input values “a” and/or coefficients “c” are zero. Such values “a” and “c” may be represented by 4-bit nibbles. For 8-bit (Aa) by 8-bit (Cc) multiplications, multiplications may be performed in four stages, A*C, A*c, a*C, a*c. It is contemplated that Aa and Cc are distributed in some kind of distribution (such as a Gaussian distribution), where values near zero are most common, and the values farther away from zero are less common. Accordingly, values may be quantized, such that if a value is greater or equal to +/−16, it is rounded to the nearest multiple of 16. In this way, a lower nibble for such numbers will always be zero and power will be saved when processing this nibble. In this way, all small values, less than 16, will have their MSNs=0. All large values, greater or equal to 16 will have their LSNs=0. When multiplication is performed on the basis of nibbles, this kind of rounding can be used to force a significant number of nibbles to zero, thereby saving power at the cost of some accuracy. If rounding on the basis of +/−16 causes too much loss in accuracy, then quantization at +/−32 or other value may be used.

FIG. 17 shows a cache arrangement 2500 to facilitate communications among memory allocated to different PEs. The cache arrangement 2500 includes a plurality of caches 2502, each associated with a different set of memory blocks (not shown). The selection of which cache 2502 and/or memory cells to read/write from/to may be made by activation of row and column lines.

For example, with reference to FIG. 14 , each cache 2502 may be used as a cache 2204, 2206 associated with any suitable number of blocks 2200, 2202 of memory cells. Communications provided for by switches 2208, 2218 in the example of FIG. 15 may be replaced or augmented by the components discussed below.

The caches 2502 are in mutual communication via a write bus 2504 and a read bus 2506. A write multiplexer 2508 puts signals onto the write bus 2504 and a read multiplexer 2510 takes signals from the read bus 2506.

The write multiplexer 2508 selectively takes input from the read bus 2506, a read bus of an adjacent cache arrangement of an adjacent PE above the present PE, at 2512, and a read bus of an adjacent cache arrangement of an adjacent PE below the present PE, at 2514. As such, the write multiplexer 2508 may be controlled to write to a cache 2502 from another cache 2502 of the same arrangement 2500 or a cache of a PE in an adjacent row.

The write multiplexer 2508 also selectively takes data from the PE registers, at 2516, so that accumulated results “d” and/or input values “a” may be written to memory.

The write multiplexer 2508 may be controlled, at selection input 2518, by a controller associated with the row or bank of PEs.

The read bus 2506 takes input from the caches 2502 and provides same to the write multiplexer 2508, a write bus of the adjacent cache arrangement of the adjacent PE above the present PE, at 2512, and a write bus of the adjacent cache arrangement of the adjacent PE below the present PE, at 2514.

The read multiplexer 2510 may provide input to the PE registers, at 2520, so that the PE may read coefficients “c” and/or write input values “a” from memory.

The cache arrangement 2500 allows for cache-to-cache communications between memory blocks associated with different PEs as well as blocks associated with the same PE. The cache arrangements 2500 of a top and/or bottom row of PEs in a bank 102 (FIG. 1 ) of PEs may be connected to respective cache arrangements 2500 of a bottom and/or top row of an adjacent bank 102 of PEs, so as to facilitate communications among different banks 102 of PEs. Additionally or alternatively, the cache arrangements 2500 of a top and/or bottom row of PEs in a bank 102 may be connected to an I/O bus, such as bus 1604 (FIG. 12 ), so as to facilitate communications among different banks of PEs.

The cache arrangement 2500 may additionally provide redundancy in case of bad memory cells. Each cache 2502 may serve a number of rows (e.g., 32) of memory cells. A given memory block may be assigned to compensate for bad memory cells in another block. This memory block may have a number of rows (e.g., 2) reserved to replace rows containing bad cells.

A table of virtual registers may be maintained for each cache 2502. The table may map logical addresses to caches 2502.

FIG. 18 is a block diagram of a computing device 1800 including an array of PEs 1802 with memory cells 1804 and cache memory 1806 and connections there-between. The computing device 1800 may include any number of PEs 1802, each with its own connected blocks of memory cells 1804 and cache memory 1806. Examples of PEs with memory cells and cache have been described with regard to FIGS. 14, 15, and 17 , which may be referenced for further description. The techniques described below may be used in the other examples discussed herein, such as those of FIGS. 14, 15, and 17 , and vice versa. The PEs 1802 may implement a row 104 of PEs in a bank 102, where a plurality of banks 102 form a computing device, such as discussed elsewhere herein (see FIG. 1 for example).

The PEs 1802 are mutually connected to share data, such as described elsewhere herein, so as to perform SIMD operations, such as multiplying accumulations. Blocks of memory cells 1804 are connected to each PE 1802 to store data related to the SIMD operations, such as coefficients, input/activation values, and accumulated results, performed by the PEs 1802. A cache 1806 is connected to each PE 1802 to cache data of a respective block of memory cells 1804. A PE 1802 may be connected to its memory cells 1804 through its cache 1806. In this example, each PE 1802 includes a plurality of caches 1806 each associated with a different block of memory cells 1804. Any number of caches 1806 and blocks of memory cells 1804 may be used for a respective PE 1802.

A cache (first cache) 1806 of a given PE (first PE) 1802 is connected to an adjacent cache (second or third cache) 1806 of a PE 1802 that is adjacent the given PE 1802. Adjacency may include any one or combination of immediately adjacent, second adjacent, third adjacent, and so on. Such connections may have special cases at or near the ends of the array of PEs. An end of the array at or near a controller 1810 may have connections with the controller 1810.

The connections of caches 1806 of adjacent PEs 1802 allow sharing of recently or frequently used data among adjacent PEs 1802. While the PEs 1802 may be mutually connected to share data, such as data stored in PE registers, and described elsewhere herein, it may be useful to provide direct memory communication via the caches 1806.

The computing device 1800 may further include a multiplexer 1812 connecting each PE 1802 to its caches 1806. The multiplexer 1812 may implement cache read and/or write functionality between the PE 1802 and its caches 1806 and between the caches 1806 of adjacent PEs 1802. The multiplexer 1812 may include a write multiplexer and/or a read multiplexer, as discussed above with regard to FIG. 17 .

Regarding writing, the multiplexer 1812 (or write multiplexer 2508 of FIG. 17 ) may include an output connected to the cache 1806 of the PE 1802 to which the multiplexer 1812 belongs. The multiplexer 1812 (or write multiplexer 2508) may further include selectable inputs connected to a register 1814 of the same PE 1802 and to a cache 1806 of an adjacent PE 1802.

Regarding reading, the multiplexer 1812 (or read multiplexer 2510 of FIG. 17 ) may include an output connected to a register 1814 of the PE 1802 to which the multiplexer 1812 belongs. The multiplexer 1812 (or read multiplexer 2510) may further include selectable inputs connected to the cache 1806 and to a cache 1806 of an adjacent PE 1802.

As such the multiplexer 1812 of a respective PE 1802 may read from its (first) cache 1806 and (second, third) caches 1806 of adjacent PEs 1802 and provide such data to its PE's registers 1814. The multiplexer 1812 may further write to its (first) cache 1806 from its PE's registers 1814 and from (second, third) caches 1806 of adjacent PEs 1802.

The multiplexer 1812 selection input that determines cache read source and/or write destination may be controlled by a controller 1810, which may be a SIMD controller of the row or bank of PEs 1802.

The controller 1810 may control the PEs 1802 to perform a multiplying accumulation that uses coefficients, input/activation values, and accumulated results. Accordingly, the controller 1810 may be configured to control a multiplexer 1812 to write to its (first) cache 1806 accumulated results and/or input values of the multiplying accumulation. The controller 1810 may further be configured to control the multiplexer 1812 to read from its (first) cache coefficients and/or input values of the multiplying accumulation. Input values and/or coefficients, for example, may be shared among adjacent PEs 1802 via the cache connections provided by the multiplexers 1812 of the PEs 1802 and as controlled by the controller 1810.

FIG. 19 shows a bank 2600 of PEs 108 arranged in rows 104 and connected to a controller 2602 that may be used to control SIMD operations of the PEs 108. The controller 2602 may be connected to end-most PEs 108 of each row 104, for example, two adjacent end-most PEs 108.

The controller 2602 may be configured to control the PEs 108 as discussed elsewhere herein.

An ALU 2604 may be provided to each row 104 of PEs 108. The ALU may be connected to end-most PEs 108, for example, two adjacent end-most PEs 108. Local registers 2606 may be provided to each ALU 2604.

Each ALU 2604 may be configured to perform an operation on the respective row 104 of PEs 108. Example operations include move, add, argmax, and maximum/minimum determination. The intermediate and final results of such operation may be stored in the associated registers 2606. The ALU 2604 may be purposefully limited in its operational capacity, so as to reduce complexity, and addition and argmax operations are contemplated to be quite important for neural networks.

Operations on a row 104 of PEs 108, as performed by the ALU 2604, may be facilitated by copying data between neighboring PEs 108, as discussed elsewhere herein. For example, operations may be performed on data as the data is shifted towards and into the end-most PEs 108 at the ALU 2604.

The controller 2602 may control the ALUs 2604 in a SIMD fashion, so that each ALU 2604 performs the same operation at the same time.

The local registers 2606 may also be used as staging for reading and writing from/to the respective row 104 of PEs 108.

The controller 2602 may further include an ALU 2608 to perform an operation on the results obtained by the row-based ALUs 2604. Example operations include move, add, argmax, and maximum/minimum determination. The bank-based ALU 2608 may include registers 2610 to store intermediate and final results. As such, results obtained by individual PEs 108 may be distilled to row-based results, by ALUs 2604, that may be further distilled to a bank-based result, by the ALU 2608.

As should be apparent from the above discussion, the techniques discussed herein are suitable for low-power neural-network computations and applications. Further, the techniques are capable of handling a large number of computations with flexibility and configurability.

It should be recognized that features and aspects of the various examples provided above can be combined into further examples that also fall within the scope of the present disclosure. In addition, the figures are not to scale and may have size and shape exaggerated for illustrative purposes. 

1-7. (canceled)
 8. A computing device comprising: a plurality of rows of processing elements to perform single instruction multiple data (SIMD) operations, wherein the processing elements of each row are mutually connected to share data; and a row arithmetic logic unit (ALU) at each row of the plurality of rows of processing elements, the row ALU of a respective row being configured to perform an operation with processing elements of the respective row; wherein the row ALU is connected to one or more end-most processing elements of the respective row.
 9. The computing device of claim 8, wherein the row ALU is connected to two end-most processing elements of the respective row.
 10. The computing device of claim 8, wherein the row ALU is configured to perform addition with data contained in the processing elements of the respective row.
 11. The computing device of claim 8, wherein the row ALU is configured to perform argmax with data contained in the processing elements of the respective row.
 12. The computing device of claim 8, further comprising registers connected to the row ALU to store a result of the operation.
 13. The computing device of claim 8, further comprising a bank ALU connected to the row ALU of each row of processing elements, the bank ALU being configured to perform an additional operation with results obtained by row ALUs of the plurality of rows of processing elements.
 14. The computing device of claim 13, wherein the bank ALU is configured to perform addition with results obtained by the row ALUs.
 15. The computing device of claim 13, wherein the bank ALU is configured to perform argmax with results obtained by the row ALUs.
 16. The computing device of claim 13, further comprising registers connected to the bank ALU to store a result of the additional operation. 